Topological K-(co-)homology of classifying spaces of discrete groups

Details Topological K-(co-)homology of classifying spaces of discrete groups Topological K-(co-)homology of classifying spaces of discrete groups

2012-01-23

arxiv.org/abs/1201.4763v1

Mathematics

K-Theory and Homology

23 pages

Scientific paper

Let G be a discrete group. We give methods to compute for a generalized (co-)homology theory its values on the Borel construction (EG x X)/G of a proper G-CW-complex X satisfying certain finiteness conditions. In particular we give formulas computing the topological K-(co)homology of the classifying space BG up to finite abelian torsion groups. They apply for instance to arithmetic groups, word hyperbolic groups, mapping class groups and discrete cocompact subgroups of almost connected Lie groups. For finite groups G these formulas are sharp. The main new tools we use for the K-theory calculation are a Cocompletion Theorem and Equivariant Universal Coefficient Theorems which are of independent interest. In the case where G is a finite group these theorems reduce to well-known results of Greenlees and Boekstedt.

Affiliated with

Also associated with

No associations

Rating

Topological K-(co-)homology of classifying spaces of discrete groups does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Topological K-(co-)homology of classifying spaces of discrete groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Topological K-(co-)homology of classifying spaces of discrete groups will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-498159